Vanishing capillarity limit of the compressible non-isentropic Navier-Stokes-Korteweg system to Navier-Stokes system

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• 作者：Xiaofeng Hou^a ; ^{xiaofengh0513@163.com} ; Lei Yao^b ; ^{yaolei1056@hotmail.com} ; ^{leiyao@nwu.edu.cn} ; Changjiang Zhu^c ; ^{machjzhu@scut.edu.cn}
• 关键词：Compressible nonisentropic fluid model of Korteweg type ; Vanishing capillarity limit ; Smooth solution
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：1 April 2017
• 年：2017
• 卷：448
• 期：1
• 页码：421-446
• 全文大小：494 K
• 卷排序：448

文摘

In this paper, we consider the three dimensional compressible nonisentropic fluid model of Korteweg type. We mainly present the vanishing capillarity limit of smooth solution to the initial value problem. Based on the uniform estimates with respect to the capillary coefficient κ, we show the unique smooth solutions of the three dimensional Korteweg model converges globally in time to the smooth solution of the three dimensional compressible nonisentropic Navier–Stokes system, as κ   tends to zero. Also, we give the convergence rate estimates in H2H2-norm with respect to κ.